Necessary and sufficient conditions for Pareto optimality in differential games

P.V. Reddy, J.C. Engwerda

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.
Original languageEnglish
Title of host publicationProceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010)
EditorsP. Cardaliaguet, R. Cressman
Place of PublicationBasel
PublisherBirkhauser
Publication statusPublished - 2011

Publication series

NameAnnals of the International Society of Dynamic Games

Fingerprint

Pareto Optimality
Differential Games
Pareto Optimal Solution
Infinite Horizon
Weighted Sums
Pareto
Necessary Conditions
Optimal Control Problem
Sufficient Conditions
Pareto Solutions
Transversality Condition
Constrained Control
Autonomous Systems
Optimal Control
Scalar
Game

Cite this

Reddy, P. V., & Engwerda, J. C. (2011). Necessary and sufficient conditions for Pareto optimality in differential games. In P. Cardaliaguet, & R. Cressman (Eds.), Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010) (Annals of the International Society of Dynamic Games). Basel: Birkhauser.
Reddy, P.V. ; Engwerda, J.C. / Necessary and sufficient conditions for Pareto optimality in differential games. Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010). editor / P. Cardaliaguet ; R. Cressman. Basel : Birkhauser, 2011. (Annals of the International Society of Dynamic Games).
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Reddy, PV & Engwerda, JC 2011, Necessary and sufficient conditions for Pareto optimality in differential games. in P Cardaliaguet & R Cressman (eds), Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010). Annals of the International Society of Dynamic Games, Birkhauser, Basel.

Necessary and sufficient conditions for Pareto optimality in differential games. / Reddy, P.V.; Engwerda, J.C.

Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010). ed. / P. Cardaliaguet; R. Cressman. Basel : Birkhauser, 2011. (Annals of the International Society of Dynamic Games).

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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N2 - In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.

AB - In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.

M3 - Conference contribution

T3 - Annals of the International Society of Dynamic Games

BT - Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010)

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Reddy PV, Engwerda JC. Necessary and sufficient conditions for Pareto optimality in differential games. In Cardaliaguet P, Cressman R, editors, Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010). Basel: Birkhauser. 2011. (Annals of the International Society of Dynamic Games).